2/5 − 1/3 = 1/15, about 0.067 as a decimal.
Answer
\frac{2}{5} - \frac{1}{3} = \textcolor{#0b5c56}{\frac{1}{15}}The difference is 1/15 in simplest form.
\displaystyle 0.0\overline{6} (the 6 repeats forever, about 0.0667)1 of 15 equal parts
The problem
\frac{2}{5} - \frac{1}{3}Write both fractions over 15. List multiples of each denominator until they meet:
Multiples of 5: 5, 10, 15
Multiples of 3: 3, 6, 9, 12, 15
The least common denominator is 15. Multiply the top and bottom of each fraction by the same number, so its value doesn't change.
\begin{aligned} \frac{2}{5} &= \frac{2 \times 3}{5 \times 3} = \frac{6}{15} \\[10pt] \frac{1}{3} &= \frac{1 \times 5}{3 \times 5} = \frac{5}{15} \end{aligned}= \textcolor{#0b5c56}{\frac{6}{15}} - \textcolor{#0b5c56}{\frac{5}{15}}Subtract the numerators. Keep the denominator 15.
= \frac{6 - 5}{15} = \textcolor{#0b5c56}{\frac{1}{15}}Check that it can't be simplified. 1 and 15 have no common factor other than 1, so this is the simplest form.
\text{GCF}(1, 15) = 1\begin{aligned} &\frac{2}{5} - \frac{1}{3} \\[8pt] &= \frac{2 \times 3}{5 \times 3} - \frac{1 \times 5}{3 \times 5} && \textcolor{#5b6660}{\textsf{LCD}} \\[8pt] &= \frac{6}{15} - \frac{5}{15} \\[8pt] &= \frac{6 - 5}{15} && \textcolor{#5b6660}{\textsf{subtract}} \\[8pt] &= \textcolor{#0b5c56}{\frac{1}{15}}\end{aligned}| Simplest form | 1/15 |
|---|---|
| Decimal | 0.0666… (the 6 repeats forever) |
| Percent | ≈ 6.67% |
| Same fractions | 1/3 + 2/5, 1/3 × 2/5, 2/5 ÷ 1/3 |
2/5 − 1/3 = 1/15 (0.0667 as a decimal).
Write both over a common denominator, subtract the numerators and simplify. The working above shows each step.
Other fractions, mixed numbers or up to five terms: use the Fraction Calculator.